Example

First note, as a beginning to each of the following arguments, $a_1 \equiv b_1 \pmod{m}$ implies $b_1 = a_1 + mk_1$ for some integer $k_1$, while $a_2 \equiv b_2 \pmod{m}$ implies $b_2 = a_2 + mk_2$ for some integer $k_2$.